he work done by the centripetal force on an object with a mass of 1 kg moving with a constant velocity of 4 m/s into a circular path of radius 0.6 m for one full cycle is

The formula for centripetal force is Fc = mv^2/r, so multiply 1 kg with (4 m/s)^2 and divide that by the radius 0.6m to get 26.67N. Now this is where things get a little confusing. Technically speaking work is force multiplied by displacement which is the total distance from the beginning to the end. Since the object didn't actually change position the work would be 0 joules. I'm not sure if that's what the question wants but that's what it would be. Let me know if you have any questions.